It was really hard to find out what the guy was going on about, but...well, it kinda sounds like he's in cloud-cuckoo-land with some of that stuff about exercise. Most of it, to be blunt.
There's overwhelming evidence that exercise aids in weight loss and maintenance, so you can toss Myth #1 aside from the get-go. There are a lot of places you can go to double-check this, but the easiest way is just to do a Google search and add the phrase "site: .gov" or "site: .edu" (minus the quotes) at the end of your search tags. This will bring up credible, peer-reviewed sources of information from government and university sites. That includes the Centers for Disease Control and Prevention, the Mayo Clinic, National Institutes of Health, and multiple specific studies from universities of your choice.
Y'know...I was going to go through and "myth-bust" all his myths, but when I got to the link about "marathon runner dies, 9,000 spectators are just fine," under Myth #2, I gave up. This guy doesn't understand science, statistics, anatomy, physiology, or much of anything else. He's an anti-science nutter who probably thinks the world is hollow, 5,000 years old, and filled with UFOs.
He may make some good points about diet and exercise here and there in his rants, but look at it this way: even a stopped clock is right twice a day. He's bound to get a few things right just because he rambles so much.